{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ZDT\n",
    "\n",
    "The ZDT <cite data-cite=\"zdt\"></cite> problem suite is based on the construction process\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{split}\n",
    "\\min && \\; f_1(x)\\\\[2mm]\n",
    "\\min && \\; f_2(x) = g(x) \\, h(f_1(x),g(x))\n",
    "\\end{split}\n",
    "\\end{align}\n",
    "\n",
    "where two objective have to be minimized. The function $g(x)$ can be considered as the function for convergenece  and usually $g(x) = 1$ holds for pareto-optimal solutions (except for ZDT5).\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt1:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ZDT1\n",
    "\n",
    "This is a 30-variable problem ($n=30$) with a convex Pareto-optimal set:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\begin{split}\n",
    "f_1(x) &= \\, & x_1 \\\\\n",
    "g(x) &=& 1 + \\frac{9}{n-1} \\; \\sum_{i=2}^{n} x_i \\\\\n",
    "h(f_1,g) &=& 1 - \\sqrt{f_1/g} \\\\\n",
    "\\end{split}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "$$0 \\leq x_i \\leq 1 \\quad i=1,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optimum**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$0 \\leq x_1^* \\leq 1  \\quad \\text{and} \\quad x_i^*=0 \\; \\text{for} \\; i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt1"
   },
   "outputs": [
    {
     "data": {
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LLfDCC1HaUZIkSXmlMFbWAY4DhgM3JEnSERgHbEvUYP8COHep8eMK2iTzIE3T95MkuRvoBXyQJMlTwLdAQ2BvoAJwfZqmYwtpziVTw4Zw+eXZ+/vui7KNZcrEqvuRR0Lt2hGgX3ghfPBBrMq/8kpRzViSJEkrUCjBesHq+lbARUBnoAswFRgA9EvT9NdVfNWRRG764cBuQHVgJvAOcHuapqtUDUYF0jQbuN90U+SsZxx+OOy6a6y8v/pqBO1bb10k05QkSdLyFdbKOmmaTiJWxVdlbLKC5ylwT8GfVtfo0TBuHKy7LvTuvWx/vXpwxBHQvz88+KDBuiRJUp7JqzrrKmTTpkXbogWUL7/8MVtsseRYSZIk5Q2D9ZIss2l03LgVH5b06adLjpUkSVLeMFgvybbcEho3hilT4P77l+3/6Se48864PvDA3M5NkiRJK2WwXpKVKROHIgEcfTRcdFGccjp3LjzxBGy/PUyfDk2bwgMPRP76JZfApElFO29JkiQBkMSeztIhSZKRrVq1ajVy5MiinkrupGkE7Ndeu/z+ChVg/lLnTJUpEzXbr702arRLkiTpL2ndujWjRo0alaZp69V5jyvrJV2SwDXXwMsvw157QbVqsdm0SROoUiUC9Y03hosvhttugwMOiN8MGAAnnVTUs5ckSSrVDNZLi112gaefhlmzIkDfZptIh+naNTagnnceHHUUPPJI1F0vXx5uvhnGjy/qmUuSJJVaBuul0a+/wmOPxQr6wIFQseKS/TvsAIcdFtd33JH7+UmSJAkwWC+dvvkmVtdbtIAGDZY/pmvXaMeNy928JEmStASD9dIoc0DSjBmxAXV5fvst2goVcjMnSZIkLcNgvTRq2hTWXx+++w5ee23Z/jSFu++O6512yu3cJEmS9P8M1kuj8uXhmGPi+rDDYMSIbN/s2XD66fDWW1CuHJx/foxv1ChqsP/8c9HMWZIkqRQyWC+tzjwzDkWaPBm22w622AI6d4Z69eC662LMggWRKrNgAXz9dQTum28On31WtHOXJEkqJQzWS6vKleGll6BvX6hRA0aPjvuZM7NjTjwRvvgC5s2DYcOgTRuYMiU2n/7+e9HNXZIkqZQwWC/NKleGq6+O1fXXXoMhQ6Bdu+g77zy44YY4PKlSJdh11xjTvDlMnBilHyVJkrRGGawLqlaNjaTbbQfvvhsVYE47bdlxlSvDySfH9cMP53aOkiRJpZDBurJ++SXaDTaAWrWWP6ZFi2inT8/NnCRJkkoxg3Vl1a0bp5pOnrziqi8ffxzt2mvnbl6SJEmllMG6smrWhC5d4M8/4corl+2fPRuuuSaux4yBTTaB9u3htttgzpzczlWSJKkUMFjXks48E8qUiaD8iCPgo48i5eWpp6Js4zffxLhvv43rd9+Nmu3//Cd8+WXRzl2SJKmEMVjXkjp0gDvugLJl4xTTVq0iPaZ796i1DlGf/YUXYMIEuP9++Mc/oq9zZ5g7t2jnL0mSVIIYrGtZvXrBJ59Anz6w4YZRh7127ejr3h3efDMC88aN4V//ihNQmzeHr76ySowkSVIhMljX8jVvDjffDJMmxWbTzCFIl10Wm1AXV60anHFGXA8enNt5SpIklWAG61q5mTMjvWWttWCzzZY/Zpttop06NXfzkiRJKuEM1rVy1apFDvusWfDDD8sfM2FCtJUrR3nHKVNyNz9JkqQSymBdK1ehAnTrBmkK/fsv279wIfz733E9ejRsuSXUqxenog4bltu5SpIklSAG61o1p54a7dVXQ9++cXASxEbUFi3gs8/ivlo1aNkyVtjfeAN22w1uvbVIpixJklTcGaxr1Wy/Pdx0U1xfe21UialSJWqvf/55PD/uOPjxxwjgf/gBLrgg+/zTT4tm3pIkScWYwbpW3fHHwzvvwP77Q/nyMG8elCsXfX36wMCBEcBDbEbt1w+OPBIWLYrKMpIkSfpLDNb117RrB48+GoH6rFmRzw7ZnPWl9ekT7Qsv5GZ+kiRJJYjBuv6esmWhatXsiaXrrbf8ceuvH60nm0qSJP1lBuv6+5IENt44rl97bfljnn022jlzoGFDaN0arroKpk/PyRQlSZKKM4N1rZ4jj4z23HNh9uwl+954A044Ia7nzIFvv4VRo+Css+JwpREjcjpVSZKk4sZgXavn2GOhfn348MOoDNO/P7z4YgTvHTtGDfbKleHBB+HLL+GZZ6B9+1hZ79IlWwJSkiRJyyhX1BNQMVenDrzyCuyxB3zxBZx++pL9VatG2caGDeO+UaMI0rt0gZdfjioxl16a82lLkiQVB66sa/U1aQJjx8KTT8KBB8Kuu0KNGtH3yCPZQD2jXDk4//y4Hjw4p1OVJEkqTlxZV+EoVw722Sf+AGrWjLZNm+WP32abaKdOXfNzkyRJKqZcWdeaUatWtBMmLL9/9OhokyRSY1q3hssug2nTcjM/SZKkYsBgXWvGvvtGe801kKZL9k2YEJtPARYsgK+/jiox554bKTWvv57buUqSJOUpg3WtGccdB5UqwRNPwGGHxeZTiNz21q2zZR4vvxzGj4chQ2DnnWHmTOjWbcUr8pIkSaWIwbrWjE02ic2lFSvCffdFXfUqVaBFC5g1K8bcfTecfTZsuil07RrVYbp3j0D++uuLdv6SJEl5wGBda063blF//cgjI1CfNy9y1AEuuQQOP3zJ8WXKQL9+cX3ffbBoUU6nK0mSlG8M1rVmtWgBd9wRq+mzZsHGG8fzAw5Y8fgqVWLsuHHwyy+5m6skSVKeMVhXbpQpA9WqZeuvrygn/bXXYO7cuG7RIg5dat8+ct8lSZJKGYN15VamSsx11y2b5vLaa7Dbbtn7evVik+q778J++0V+uyRJUilisK7c6t0bqleHV16J004/+yyejx0LXbpEKUeAxx6D77+Hn36C/v2hfHm48kpX2CVJUqlisK7cWnddeOopqFoVHn8c/vGPSI9p0QL++CPGDBwYK+kQfaeeCldcEfcDBhTNvCVJkoqAwbpyr2PHOATp2GMjGJ8zJ1sl5qKLokb70o46KspAvv02/PprbucrSZJURAzWVTQ23RRuuQVmzIi/LbeM5506LX989epQs2ZcH3ssnHQSvPCC5R0lSVKJZrCuolWmDKy1FtSvH/fvvrvsmAULoib7jz/G/aOPwo03Ro578+YwZkzOpitJkpRLBuvKD5kDkvr3hx9+WLLv+OPh3nvjukEDGDQILrwwAvzx42GnneDrr3M5W0mSpJwwWFd+6NoVttkGJk+GrbaCa6+F//432ttuizGVKsHQoXDMMfCf/0Sg3qkTTJ8eJ6JKkiSVMAbryg/lysFzz2UD9r59oU2baAEqVIDnn4/qMRmVKkXlGICHHoKZM3M/b0mSpDXIYF35Y511YPhweOYZ2GcfaN0aatWKvsGDI91laY0bQ9Om8PvvcPfd8NJLsWFVkiSpBDBYV34pWxa6dYMnn4QPP4S2beP5woXLH//WW9l89VNOgc6dYYMNovyjK+2SJKmYM1hXfsuspt99N6Tpkn3PPx812+fPjzrtu+8O224Lc+dGWcgddzRglyRJxZrBuvJbr15QpQq88gqcc04E4hDtwQdHWUeAc8+N4H3ECBg9OtJjPvooqsZIkiQVUwbrym+1a8Ndd0U99iuvhHr1or5606bZVfMOHSJYz/jnP2PDKcRvMwG+JElSMWOwrvx34IHw4otRKea33+Lk0kmToq9jx+irVGnJ32y1VVSOmTEjDlH69FP488/cz12SJGk1GKyreNh116i7PmYMPPtsNpf9sMOgcuVlx3/9NUybFte9ekHLlrDRRnDBBa60S5KkYsNgXcVLixaw557ZYP2555Yd8+mnsPXW8NNPcb/ZZnHa6Y8/wsUXwy67wJw5uZuzJEnS32SwruKpV68o8/j440sG7IsWwf77wy+/xP2uu8Lnn8PEifD66xG0v/debFaVJEnKc4UWrCdJsmGSJHclSTIlSZI/kiSZmCTJ9UmS1Pob72qVJMmDSZJ8X/CuH5MkeTNJkkMLa74q5jbcEM4+O8o5dusGe+wBN90UQfznn8eY6tXhuuviOkmilOOTT8b93XfDrFlFMnVJkqRVVa4wXpIkSSNgOLAO8AzwObANcDLQOUmSdmmaTl/Fd50ADAB+BYYCk4HaQAugCzC4MOasEuDii2N1/YorYOjQ+MuoUQNefjk2mS6udetIkfngA7j1VmjTJqrHrLVWbucuSZK0CgolWAduJgL1k9I0vTHzMEmS/sCpwKXAsSt7SZIknYAbgJeB/dI0nbVUf/lCmq9KgiSBfv3ghBPgvvtg/PhIcRkzBi66KILypX39NUyeHNdnnBFt1arQs2cE/3Xr5m7+kiRJK7HaaTAFq+qdgInAwKW6/wPMAXomSVJ1FV53NTAP6LF0oA6Qpqm197SstdeG006LlfKePePZ668vO27cuDjhdMqUuG/ZErbYIjabDhoEbdvGJlRJkqQ8URg56wVlORiWpumixTsKAu53gSpAm//1kiRJWgD/BIYBvyRJslOSJH2TJDk9SZKOSZK4GVYr17MnlCsHzzwTp55mpCkccgj8/HPct2wJn3wSp5x++ilsvjlMmAAnnlg085YkSVqOwkiD2ayg/WIF/ROIlfdNgVf/x3syOQvTgDeADkv1j0mSpHuapl+ubEJJkoxcQVfTlf1Wxdx668Uq+1VXwe67R/DerRuMGhV/EOkzV1+d/c0//hG12xs1ig2okyfHSamSJElFrDBWq2sUtDNW0J95XnMl71mnoD0SaAh0LXj3psD9QEtgaJIkFf72TFU6XHYZnHwyLFgQVV/22Sfy0SFW3R96CHbbbcnf1K8PnTrBwoVw5pnQvz+8/XasyEuSJBWRwtpgWhgy/3AoCxyUpul7BfczC0o2NgW2AvYFHvpfL0rTtPXynhesuLcqnOkqb5UtC9dfD8cfD7ffDmPHRorLhAnQty8ceOCyv3nnHXj33bh+8MH4g1h1v/VWaNcud/OXJEkqUBgr65mV8xor6M88/20l78n0/7BYoA5AmqYpURISoiSktHJNmkQ6zNCh8O9/x7M331x23DvvxKmmMwr+R3nvveHYYyOlZuzY6MsE8pIkSTlUGMH6+IJ20xX0NyloV5TTvvR7VhTU/1rQVl7FeUlZ++8ftdTfew8GL1aqP00jMP/jj7jfbLPIW7/lFvj22zhk6fffY4wpMZIkKccKI1jP1MjrtHTFliRJqgPtgLnAiJW8ZwRR5rHhCso8tihov1mNuaq0qloVLrkkrg87DPbcM/LZ+/aN1fOMq6+ODagAFSpE0L7uulExxtV1SZKUY6sdrKdp+hVRbrEhcPxS3f2AqsB9aZrOyTxMkqRpkiRLVGZJ03QucCdQCbgkSTIREyRJ0hI4HFgAPL66c1YpdcIJEYxXqABDhsARR8RGUoDy5WPj6Z57LvmbihVhxx3jukcP2Gor6N07TkCVJElaw5K0EP5f+wUHIw0nKro8A4wDtiVqsH8BtE3TdPpi41OANE2Tpd6zFvAmsAXwX6JG+7pAdyL95ZQ0TQesxjxHtmrVqtXIkSuq7KhSYdo0uOce+PjjOPV01Cg48ki4445lx15yCZx//vLfc9RRsfJetuwana4kSSp+WrduzahRo0atqPDJqiqUg4YKVte3Au4hgvTTgUbAAKDN4oH6St4zE9geuAyoDZwA7AG8A+y2OoG69P/WWSfKMz74IAwo+B+pIUOyeesZt922ZKB+ww2RCnP66VCpUlSayWxclSRJWgMKZWW9uHBlXctIU/jnPyMn/fDDYdCgSH35809o2BCmTIlxLVvC6NHZfPbXX4edd46xkydDnTpF9QWSJCkP5dXKulRsJUnUUa9UKVJj6teHY46BvfbKBuoVK8aYZLGsrZ12ioOV/vgjDlwaNgy++65IPkGSJJVcButS27bw2muxej5tWqS/vPBC9NWqFavo22235G9+/RV++SWuBwyIwL1hQ+jaFT75JKfTlyRJJZfBugQRjI8eHQckXXcdHHpoPN9882UD9V9+ge23z1aEqVcvKsZUqADPPx+nnY5YWaVSSZKklTNYlzKSJALtU06B66+HypXhjTciiF/cGWdEbfZMWsywYbH6/v33cMAtb7BOAAAgAElEQVQBMHs2HHwwLFyY80+QJEkli8G6tDy1asWGU4AuXeDppyP4nj4d7r8/nqcpdOoEzZvHfd260bfJJjBxIgwdWhQzlyRJJYjBurQi11wDHTrERtN99okAvmFDmD8/+ps1g8GDl/xN+fKw++5xffjhsPHGkc/++OOwYEEuZy9JkkoAg3VpRapUgZdeiqC9USOYNStSXACaNIHhw2HddZf8zY03ws03x/Wvv8YK+7BhsP/+UUFmxoycfoIkSSreDNal/6VSpTgEacIE+PHHyGGHuC5XbsmxTz8NJ50U6TEAp54KX3wRhymtv35sXj344JxOX5IkFW8G69KqSJI4+XSHHWIT6syZsdF00aLoT9Oot55RqRKcd16swJ94Irz3Hqy1VpSE/PDDovkGSZJU7BisS3/VlVdGmcZBg2DLLaF//wjUR43KjrngAqhdO3vfoAH06hXXxx4bAfx110Vdd0mSpBUot/IhkpbQrh089xz07BkHIJ1+erYvSSJwP/vsJX8zfnykyQCMHBl/EONOOw0uvRTK+G9nSZK0JKMD6e/o1Am++w7uuw9694Y99ojn660XAXimBjvEuB12gG+/jfvNN4/V+D32gD//hCuuWDLglyRJKmCwLv1dFSvCIYfA7bfDM89EffWpU+GRR5Ycd/HFsSG1QoW4v/rq2Hz63HPw4ouxUfX662P1XZIkaTEG61JhKFMmuzp+5JGxcj5jRmxEve++eD5/fqyqd+yY/V2nTnDooXF95plwzz3w2muefipJkgCDdanw9OkTm0d//z0C95o1oU4d+OOP6G/YEJ56asnc9Llz4Ycf4vrZZ2MTaseOUdf9nnty/QWSJCnPGKxLhSVJ4kCkJ5+MA5CSJHtqaY0a8MEHcaJpxu+/x2mnzz8f97VrR1rNJptEfnuvXpEyI0mSSi2DdakwJQnss0+kssyfD7/9FptOZ8yAMWOWHHvTTfDWW5H7DnDWWZEyM2EC3HJL9tmXX+b2GyRJUt4wWJfWlHLlYkX96KPjvlcvGD06rhctilV4iDSZSpWyddjLlIl0mkMPjcOWLrwQhg2DTz/Nno4qSZJKBYN1aU076yxo0yZSW7bYIuq077knfPNNdsytt8Laa2fvFy2CKlXi+oEHYLfdoGVLaNUq0mwkSVKpYLAurWlVqsDLL8Nxx8X18OHZPPWyZaPsY6YiDMTq+VFHxQmpECUfd945Nqt+/DHsuy/ceGPuv0OSJOWcwbqUC9WqwcCBMGVKVH154AGoVStKNNaps+TYxx6Du+6KNBqIQP7VV+H77+HKK+PZySfD55/n9hskSVLOGaxLuVSjRqTA9OgReekAxx8PP/2UHXPTTUv+JjOuUqWoxd6rV6y+X3RRbGQ1l12SpBLLYF0qKn37QuPGsem0ceMIyi++GN5+O/oXLIh0mNats79JU1h//bh+6KGoyd6yZRy29NBDuf8GSZK0RhmsS0Wldm14882oyT5zZmwyveCCbH/fvtkSjhnnnAOXXRbXZctChw5Qt26UhezRI9snSZJKBIN1qShtsEGksnz8caS19O0bJ58CdOkSAXnGa69FznrmBNROnSLYnzwZbrgharyfey68/37uv0OSJK0R5Yp6ApKINJbNN4/rqlWhX78I3F97LfLcIVsBplIlmDsXjjkm7itUgBNPhK+/huuvj9X5o46Klfv27aF8+dx/jyRJKhSurEv55sQTYeONYdQoaNoUzj8/TjYdOjT6586NUo577JH9TZrCWmvF9UsvwX77xZgGDeDqq6NuuyRJKnYM1qV8U6dOrKhvuSX88ANcckmUb/zzz+jfYw94+uklU2T+/e9Io4FIk9l7b9hsM5g6NSrIHH20FWMkSSqGDNalfNSwIYwcGfXVjzsuNo9m6rEfcQRUr54dO3w4XHFFNnjfemt46ikYNy7aypXhzjvhuedy/hmSJGn1GKxL+SpJIpVl4MA4ROm88+L5uefC9OnZcQMHRlu1arRHH539/d57Z1fczz03gvpbbokDliRJUt4zWJeKiyOPhGbNYsW8efMIvh96KE5EhSj/2KpVrMJnLFoEP/4Y159+GqUfjzsuVu4POSR+I0mS8pbBulRcVK8Or7wC224L06ZFTfUePWD27Ohv0wZefDGqxWQcfzxcc032vm9f2GefWHV/4AHYbTeYNy+33yFJklaZwbpUnGywAbz3HrzxBvTpAwccAPXqRV/PnrD22tmxI0bAoEHZ0o0tWkRlmCefhLFjoX79GHPrrTn/DEmStGoM1qXiJklghx3g5pvhkUeyK+cXXwxffZUdlzn9NJPLnqnLDrDppnDddXHdr1/ktvfsCY8+CvPnr/lvkCRJq8RgXSru9tsvgvcffoCWLaF37wjkM9VffvsNttgiqshkzJkD99+f7X/mmbg/8EBo0gQ++ij33yFJkpZhsC4Vd+XKRWC+776Rf37nnZGr/uuv0b/NNvDyy1ClStynKRx0UJR1zLjvPujfP2qzf/cd7LJLnIgqSZKKlMG6VBJUrw6PPx6VYi64IFJeWraMvh12gLp1s2PfeguGDMmmxzRtCv/6F5x6KoweHZtOf/kFrrwy998hSZKWYLAulSRNm0YO+qBBcPvt8WzAABg6NDvmjjuiLVPwv/59+kQePEDFitm67LffHve1asHBB8fGVkmSlFMG61JJte22cMIJsWF0jz1gu+1i9XzIkOifNQvat88eogQwcWK2Tnuaxm9/+w0efhjato1DlSRJUs4YrEsl2YABUSWmRo0o03j99RF8A+y0E7zwQrYu+8KF0K1bVJTJrLp/9RV8+WXUZ0+SOFTpySeL5lskSSqFyhX1BCStQWXKwHnnxYr6c8/B5Mnw7ruxubRChWzeOkTgPmYM1KkD06dHzvvGG0eQfvXVsN56EbRfeGGsulesGKvttWsX2edJklTSubIulQZVq0YFmNNPj3z2ypXhpZciiM+stD/0ULSZE1FPOCGbyw4RvJctGwH9fvvBnnvGgUy9e2crz0iSpEJlsC6VNuusE6Uay5WLNJkNNoA2beCJJ6L/jz9iQ2nv3tnfvPBC5L0vXBj3HTpEvvvvv0epyA4dskG/JEkqNAbrUmm0777w2mtRT33ePPjvfyNIB+jSJYL5TN76vHlxuumff0L58vFs8GB4++0oFdm0KXz6aaTbSJKkQmWwLpVW228fhyV99x288w4MHBjPR4+GGTOy4x55JHLYN9ggAva2baFBg+hr2jQqxQDcdltsWu3cGS67DH78MbffI0lSCWSwLpV2G20E7drBscfCllvGJtR27bJB+jPPxLgpU6I966zsbxcuzNZz//NPeOONyIU/99wI6O+5J5dfIklSiWM1GEmhTBl49lnYdVf4/PPYkLq0/v2jvGPGOefEinySRIWYSy+FJk0iTWbIEOjVK6rFLP4bSZK0ylxZl5S14YbwwQcRgG+5ZdRnr149+nbcMarHZPzwQ9RtT5II9MuUgcMOg/33jzKRmZNQzz4b3n8fRo6EuXNz/kmSJBVnBuuSllStGhx3HIwaFRVevvgiKse88Ua2YgzAAw9E6st660U6zB57RCnHjEMOiQOXxo2L01S32grWXx9OOQV++SXnnyVJUnFksC7pf1tvPbjggrjeb7/YQDpgQOS0A0ydGqvvl12W/c3XX2dLOwLUrx+bUWfOjN+2awc//ZTb75AkqRgyWJe0cuedF/nolSrFBtJTTol0GYhUmVdfhX/8Izv+0ENjQ2omhebmm2OFfdQoaNEicuJPOCH33yFJUjHjBlNJK5ck8O9/wzHHRPrL+PGxMv7YYxHAN2uWHTtyJLz7bgTqs2ZFWk2HDtG35Zax8bRRo/jtlClQsSK0bh3v3mSTovk+SZLylCvrklZdnTpw0kmxAfWRR2CLLaKeeteuMHZsjHnxxWgXLYq2V6/sCjvAgw9GjnuaRn33V1+Fq66Cxo2hX794LkmSAIN1SX9XkkTAvv768NZbkd7SuDFccUX0z5kTeeuZe4BbbokV+ozjjovKMYceGu+78MLIaZckSYDBuqTVsemmUZbxmGOgalX46iuYPTv6NtoIhg2DKlXi/o8/IhiHWKEH6N49qsjcey/cf38869cvTkV9/HGYMCGnnyNJUr4xWJe0ejbcEAYNinSYsWPh449hrbVg0iR46qnsuOefh2nTorrM9Omw8caw007Z/u23h1q1olzkwQdHvfZNN4WOHeOdkiSVQgbrkgpH1arQvDlsvnl2Bf2QQyLofuSRWCmHOEwJIj2mTMF/BU2aBNttB7/+GveNG8eKe5Uq8NprkU7z/vs5/RxJkvKBwbqkwnfKKVHqsUyZCNIPOig2lkI8u/12OOCA7PgTT4Tvv4e6dbP3zz0HkyfDgQdG/nvPntlNq5IklRIG65IKX6bU47ffxir7XnvBbrvF87JloVOn7NjvvovAvEKFKPUI0KVLtDVrRj573bpxkmr16lC5MrRqFak38+bl/NMkScolg3VJa069evCf/8DTT0dJx+7d4c8/4xTU4cOjTOPbb8eKecWKsQl1jz0iDQai/4wz4Oef437u3DgV9aOPoE+fyHOfPr3ovk+SpDXMYF1S7gwaFCedjhsH7dpBgwZRtx1iVX2zzeCOO7Ljb7oJbrwxVuMhSj3OnBkpNQ0bxgFMPXrk/DMkScoVg3VJuVO3bhyEdPbZcT1pEvzyS/RVqhQHJK27btwvXAhXXx3X9etHu912kQpz8MHxnurVozxkt27x7IIL4Jtvcv9dkiStIQbrknKrZk24/PLYPPr557HK3qpVpLdceml2E+l770UwX6dOBOC1asG++2bf8803EdBD5Lw//DBcfDE0agQnn5ztkySpGCu0YD1Jkg2TJLkrSZIpSZL8kSTJxCRJrk+SpNZqvLNDkiQLkyRJkyS5pLDmKikPVKgQaS9Nm8L110P58nHCaYsWcMkl2XSYTE76tdfG5lKA0aNjw+rcuXG/7bYweHCUiixbFm64AU49NfffJElSIStXGC9JkqQRMBxYB3gG+BzYBjgZ6JwkSbs0Tf/SLrAkSaoD9wJzgWqFMU9JeWr77WHoUDj88FhpP//8bF+SwK23Qq9e2WcXXBCBepMmccrpTjtFaceePaF3b9hll8h132QTqFYtDmDaccds7rskScVEoQTrwM1EoH5SmqY3Zh4mSdIfOBW4FDj2L75zAFADuLzg95JKsl13hYkT4Zln4N13o2rMI49EJZhKlbLjpk6FIUNiJX7y5Hh28MHZ/i22iI2rX3215Op6w4axYv+vf+XiayRJKhSrHawXrKp3AiYCA5fq/g9wNNAzSZLT0zSds4rv3AvoBfQsjDlKKibKl4f99os/iJSYPn3gyCNh/PhYXf/ss8hrL1cuVte7dIF//jPGz54NO+8cgTrAOutE/5tvRo77IYfAb7/B8ccXzfdJkvQXFUbO+k4F7bA0TZc4XjBN01nAu0AVoM2qvCxJknWA24Gn0zS9vxDmJ6m4OuYY6Ns3VtkvvTTqr3frFn3z58M228D9i/3XxFVXwahR2ZNQd90V7r47UmWuvz6enXwyvP8+jB2brUQjSVKeKoxgfbOC9osV9E8oaDddxffdTszrr6bN/L8kSUYu7w9o+nffKakIJEmUb3zjDdh//wjC11orVtUh0lpqFexh//NPuO22uK5ZM9pddom2bNmo5966dVSJ2XbbWLVfe23YZx/44IOcfpYkSauqMIL1GgXtjBX0Z57XXNmLkiQ5AugGHJem6Y+FMDdJJcEOO8Cjj8JPP8GMGXDWWfG8V684ATVN4euv4ccfoUoV+PLLCOwPPDDGpSmcckocogQR7G+2GZQpE6ertm8f5R8lScozeVNnPUmShsD1wGNpmj66Ou9K07T18v6IKjWSirtzz40KMpMnQ4cO0Lx59iTTuXNjQ+rDD2dLPT72WJRzLF8+7rffPmq8T5oERx8dKTUHHQTTphXN90iStAKFEaxnVs5rrKA/8/y3lbznLmAecFwhzElSSVa5Mrz0UpyEWqdOBN6jRmX777gDOnbM3g8YEG2rVku2660HgwZBu3YR5DdsGCkz9erFuydNysnnSJK0IoURrI8vaFeUk96koF1RTntGK6L8408FhyClSZKkwN0F/ecWPHt69aYrqUSoXDlOQv3+exg+HF57Leq0Q6yiZzaP/vZb9Jcvn81NP/ro7HsefRT++9+4njcvKs1MmQJXXhlVZoYPz9knSZK0tMIoi/h6QdspSZIyi1eEKTjYqB1xsNGIlbxnMFE1ZmlNgA7Ax8BI4KPVnrGkkqNSJdhuu7hu3hxefz2qvWyySdRfr1Zwptqff0Z75pmwacHawscfRznHBQvifrPNYMyYCOovuihW7/fcM8pGZirMSJKUQ6sdrKdp+lWSJMOIWuvHAzcu1t0PqArcuniN9SRJmhb89vPF3nPS8t6fJMnhRLA+NE3T81Z3vpJKsHXXhbfeigD87bcjxWVxJ54IV1yRvb/++gjUt9kmAvxmzWIFvm3bOFG1Q4dYWW/dGipWjOoxBx8Mhx4aVWkkSVrDCuvAoeOA4cANSZJ0BMYB2xI12L8Azl1q/LiCNimk/3xJCvXrR8D+0UcRcM+dC++8E8H7N99EcF6+fFSIebRgL/vXX0d7xBHZ93z8cRzABPDdd9FOmBDB+2WXwQsvwOab5+67JEmlUqEE6wWr61sBFwGdgS7AVGAA0C9N018L4z9HklbZllvGH8SJpq1bw5AhUWP9+ONjc+m8edH/88+xybRLl7j/8Ufo3Dny3SFSYN5+Gz75JA5eGjkSdtstUmbWXjv33yZJKjUKa2WdNE0nAb1Wcewqr6inaXoPcM/fm5UkAY0aRf75XnvFinvv3kv2b7UVPPNMVIIBuOWWCOD/8Y846bRhQ2jaNP722gt22gneew923hlq146DmfbfH/bbL9JlJEkqJIUWrEtSXtt220h3efjhOAhp5syo0/7ll9CkSQTdGYMHR7twYbT/+le276efYuUd4NNPs8+feQbOOy9W7//xjzX7LZKkUiNvDkWSpDWuSpXIS3/2WXjjjWgrVYKHHoLu3eHdd2NF/fvvY/znn0e6TKYk5Ny50KlTNse9YsUoGXnzzbE5deJE2HXXbDAvSdJqMliXVHo1awaPPx41259+Gtq3jxz0TJnH2rVjI2nNmnH/wAMwbhw0aBD3a68dKTF9+kQee9u2MHUqdO0K3bpFVZonnsi+T5Kkv8hgXVLp1rVrVH0588yozV6rVvxBrJJvsUV27F13Rbv++tF2757tmz8//iAC9+eei+B+v/0i133s2DX/LZKkEsdgXZIaNowTS7/6Kk4+fecdKFcOHnkkVs0zpRu/+iraESOgQoWoKgOR277XXvDhh9l3Pv44XHstNG4caTMdO0aOvCRJf4HBuiQtrXnz2GRarlwcrNSgAdSoEZtLIarGPPBA9iTU55+HN9/MlnGsWDFW3U87Lco97rBD5LHvtVestB9+eATzpsdIklbCYF2Slufgg2MFvUePWEWfOTNb2rFz5wi6M+64I9qWLaPt2hWSxSrUVqoU7ciRkcN+771R6rFJkyglKUnSChisS9KKtG4dK+izZ0d6zCefxGr70KGR4z59eoz74otoX3892pNPjjZNoWfPqPGecdttcM01sSr/7bewyy7Z6jKSJC3FYF2SVqZ8+dh02rx5rKKXKQNXXw0bbBCbRzPBeprCZZdBhw5xP2JErKRXrx5BPsSK/emnR+DfuXP8I2DvvePv4INj1T1zsqokqdQzWJekv+Kww6K2eufOUf1l/HhYtCj6ttsOzjknO/b226PddltYsCBKO1arFs+SJOq+A4wZE4cqPfxw5LM3bAhvvZWrL5Ik5TGDdUn6q3bYIeqvT5sWJRnffz9W3997D84+G2bMiHGZFfdM4H3SSdl3HHMMPPlkNrf9hhtg4MAoFTltGuy+O4wenbtvkiTlJYN1Sfq71l47UmO23hruvDPSY668MtJjttkGPvggxs2fH8H5AQfE/dixcM89sfG0atV4tvfecNxxUf6xR484LbV796j1vsce0L9/pMxIkkoVg3VJKgw9e8KwYXGi6dy5EahnDklq1gxuvjm7in7nndG2bx+bV5s2hQ03jGeZlBqIjaevvBIbWk8/HTbaKEo+SpJKDYN1SSosHTtGPvu338Lw4XG4UpUqMG5c1Fz/7bcYN2FCtMOHR3vCCdlA/uST4cEHs/f9+0dFmo4d4x8BBx0U/xmSpFLBYF2SClv9+rHZtF07uO++qAQzYADUqxfPMsH23Lmw775w7LFxP3FiHMJUrhyss04869gx0mJefjkC/oULI2DfcstIvznttGxuvCSpxDFYl6Q1qXt3ePXV7Mr48OHRQqS+PPhg9rCle++N8o/bbx8nntarFznxENVkpkyJ659+go8/jvz2666LNJqrr879t0mS1jiDdUla0zp0iNzziROjMsw770CdOvD993D00RF8Q/ZwpA8/jLZPn2x99lNPjdKOmcD+uutihf7wwyPAP/NMGDw4l18lScoBg3VJypUGDWLVvF07eOSRqAZz772xwr7NNvDUUzFu1izYbTc444y4nzIl0mPKlo1NpgCtWsVm1rvvhhtvjGfHHhsVatZdF7p1gxdfjEBeklRsGaxLUlHo2BHefRf23BP+/DOqx8yaFX01a8Kjj0KFCnH/4IORq96+fazO16kTwT3AH39EFRqIk09//jnqtD/3XNRqP+yw+K0kqVgyWJekotKqFTz7LEyeHIH7Bx9A48ZRNebAA+HLL2PcpEnRjhwZ7THHxKo8RHrMc89lA/sbboBvvoHLLosa7vfdB//5TxzU9NtvrrRLUjFjsC5JRW399aFtW9hqq6ijXrt2pLA0aRKbRzN12WfPhl12gQsuiPsff4Q77ojDmBo3jmcbbwwNG8I558Bjj8Wzyy+P1fpataBRI7jqKpgzJ+efKUn66wzWJSmfbL45vP8+9OoVq+fjx2cD60yOe8WKcf/EE5FCs9128NlnsNZasOOO0TdnDlxxRVwvWhQr71WqxKr7WWfBDjtk675LkvKWwbok5ZtGjeCuu2LlfMyYCNi33x5+/z3y0N98M9JZpk6N8R99FO1RR0G1anF9yilReaZq1bi/6iqYOROGDIFNNomUml69opTkW29lK9JIkvJKuaKegCRpBdZaC1q0iOuHHopV808+ibZmzWy99rlzo3rMpZfG/U8/RRnHJIHNNoNRo+KQpbJloWvXqN/eujU8/XT8QZSI7N4dLrkk0m8kSXnBlXVJKg7q1YP//hfOOw/WWy9SWObPj74yZSLlJZMe88IL0bfNNhGoV60KXbpE3/Tp8K9/RWoMwAYbwLbbxkr9o49Cmzaxmi9JygsG65JUXNSuDRdfHIcp/fhjlGk8/PAIvDt3jo2oM2ZkTzrNpMcceyzUqBHXp54a+e1162b7RoyIkpC77w6//AL77AMDBsC118LQoXF6qiSpSJgGI0nFTdmykdYCMHBglHZ89VXo3Tv+MubPj8D78svjftq0OAW1TJnIi//551ixhziY6eqr4z1ffRU57xkbbRSB+/775+b7JEn/z5V1SSrOqlSJtJd7740UlgoVIh2mXMFaTI8eUL58XL/9dlSP2XzzSKmpUgX23Tf6Jk6Mg5oyqTUtW8JJJ0VJyEmT4IADoma7JCmnDNYlqbgrXx4OPRTeey9ONP399zgUCSJYP/nkCM4/+yyejR4d7amnZtNjzjorUms22STud901UmHGj8+uzB99dKyu77039O0L48bl7hslqZQyDUaSSqK+fSP4vvbaONX0hhuyfYsWwZFHQr9+cf/DD/Dkk9n0mq+/zlaEKVMmVuzLl49/BDz+ePY9114LRxwBt9ySPUFVklSoXFmXpJIoSeCaa6Keeu/ekdbSvHmcYgqxwbRMwf8JGD06NpFuumlsNq1SBQ4+OPo+/jgqyfz5Z9y3bRsnox59dKTb3HUX9OmT+++TpFLCYF2SSrJWreD226M++9ixUa+9TBm48kpo3x4GDYKXX46xmbSW//wnmx5z4YUwbx5svXXcN2sG++0Ht94ahzOVLx8Be926UL16/KOgf/+oSiNJWm0G65JUmuy2W9RTX2utOL20T59IZ8k444z4g0ijee65CMiTJJ5lgnaI0pCZFffp02H2bPj0Uzj9dNhyy0inkSStFoN1SSpt9t03arUPGhQHJB10UPak1A8/zK6Kf/NN5Levsw68/36snPfoEX2vvLJk+stOO8Gvv8JTT0W1mW++ibrtH34YVWgM3CXpb3GDqSSVRtWrwzHHxB9E6cY2beD116F+fejePbtqPnlytDfdFL+DSKOBCMhfeAHWXRdq1oxKMTvtFCUfv/hiyZX49u3hggui0owkaZW4si5JgoYN4Z13oEMHmDUr6rY/+GC2/5xzojwkwE8/xcp6xYqxQg/QqVO0aRolIX/+Oe4rVYpNqdWqxft32y3eLUlaJa6sS5JC48axaXTMmFhhnz8/KsXcfz/ceSfssEME5dOnx/gKFWJs3bqRSgMR4N99dwTpv/8OrVtHkD5rVqzGX3ppVKcZMyYC+3XXjd/Wr1903y1JecxgXZK0pJYt4w8iYJ82DYYNg86doUGDSHeBCMArVYpSjpUrx7Mbb4y2W7fYyLr22nFfvTqcdlpUjpk6dclNreecA4cdBjffHO+TJP0/02AkSStWoUJUhLn4YthgA/j22+wJqBCpMTvuGNczZ8ZJqRUrxsZSyNZrnzs3VuWnTo37unXhqqvgwAOjlOTdd8fpqIsW5ezTJKk4MFiXJP1vFSrAeefFJtSPPoqSjw89FH233QYnngiff57NU1+wIHsK6t57x7M77ogDmurVi/v11osSkQ8/HM9r1IAhQyIVZ8MNYYst4Iorsu+UpFLKYF2StGrKl48gervtIs/8xhuj/vpNN8VhSY0axbiFCyMYf2TRJ9MAACAASURBVP75CPQhDlGCyHuHCOQzfv89AnyIko+TJ8fq/TnnQNOmcaqqJJVSBuuSpL/nhBMi3eXwwyOtpVIlqFUr+jbZJNJmIALxzz6L65deivaoo6L94Yco/zhnTtzXrQvffRer7B06xGbW3XePja+vvw4ff2yqjKRSxQ2mkqS/r1WryDfPmDIlKsAMHx4HLR1zTJSFzJg+HTp2jBKOALfcAr/8EvXYP/ggSjxutFH87bZbvH/MmGxePESqzOmnx7szJ6tKUgnlyrokqfBssAG8+mqkuXzzDZx9drasI0QA/+STsakU4IEHot1442jbt8+OHTgwAnWI8R06xPu//DJOTz3ppCj/KEklmCvrkqTC1bx5pL0MHQpPPRVVYubOjRSYSZMidWbnnWPsDz9E+8QT0R5/fLRjx8bhShnly0cqzMKFsbm1d+/IlZ8yJcpGVq8em1l33TX7DwFJKgEM1iVJha9cOdhrr/iDyDM/6KCoyd6xY6TKNG0Kf/wR/QsXQt++0KZN3A8c+H/t3Xm8leP6x/HPvdvN8yCpEFKJihINogwZMp1kJsQxxqHjHH6G6Jw6nGNICUnKUDoZjukgiUzFQUmhksgUSinNpe7fH9/1vNYupWGvvffa7e/79Vqve6/nedaz1uPR7lpX133dypr/4Q8K+GvU0PZSpaBrV7j9dk1C/c9/0u85eDDsvbeOzzuB1cysGHOwbmZmBS8nR6ubNm6sjPikSXok9t1XK5wmxo3TuGSJxpNP1hijerPn7fU+fLj6vw8dqox8p07p+vdy5ZSVNzMrpvxvhWZmVjhyc7W40nffaaGlhx9WoF2unLq8dO+ufu0AS5dqHDdOiyz17Knnr72mTjHVqqXLXU4/HW66CaZPV8b+u+/URrJKFZ376KNhzJjCv14zswxwsG5mZoWrQgU49lgF5+eeC6NHKyAfOVL92kuXTq90WqqUFk5KyloeeEDj8certGaXXfRagNmztRgTwIoVqmVft06B+tFHw403FuplmpllgstgzMysaB1/PEyeDAMGaPLokiUKwFetUt/1li3TxyaZ92ShpKRf+8qVcNxx8PPPyuD/+qu60eTmqj1knz7Qt6/6udesqYx7587QrFnhXquZ2VZysG5mZkWvaVOtcjp4MKxerf7pHTvCO+9AixbQo4d6sf/0k47/7DMtvHTppXr++OPqNNO0qTLsv/6q1VOrV4cbboCpUzW5tX//9d/3kEPgoYfW7wVvZpZFXAZjZmbZIwRl1cuUUevHzp1h0SK4807Vpn/3nY6rVk393JMuMUnrx/33V0Z+v/3Sq6nedZcC9cQllyj4r1xZ7SA7dEif18wsyzhYNzOz7FS9unqzv/ceXH65OsKcfrrq2BctgkcfVW066DnAk09qvPxyjT/+CH/9q36uU0fjZZfBgw/CnDlqFfnttyq1qVEDdtxRLSbffrvQLtPM7Pc4WDczs+zWujUMHKhSl8ceU6kMQO/eUK8eHH64at5Biy+deiqcc46eDx8Oa9bAUUfBggXK3O+4o/aFoFp3gHnzVO8+b54mvHboAP/3f14h1cyKnGvWzcyseLngAgXcffqoV/urr6b3VamiuvSkrWPSyz1GBe1dumjSKsCZZ6plZOnS2vfCC+o6M3w43HYb3HqrXteggSaqtm+vbjVmZoXIwbqZmRU/xx2nxyefqIylYkW46ir44ANo105Z8Y4dlSkHldOUKqXtoCD9pZdUt163LsycqTKYPfeEf/xDK6r+61/rL9QEWnBp8GBo1KhQL9fMSi4H62ZmVnztvbceoIWWjj5agfhFF61/XAgwYoSy46De7aB+76NGKdhPzjNu3PpdY7p0UVD//PMwfrzOMWGCA3YzKxSuWTczs+1DnTrqvz5iBBx6KOy2GzRpoox6jFpoad06HTt/vsYJEzSefbYC8l9/VaeYNWu04BIo8B81Shn8I45Q+8iDDlK9fL160LUrvPKK69vNrEA4WDczs+1H2bKqRX/1Va1mOn063Huv9vXqBY0bqzd70u3l66/Vr71PHz1/4QX1a99zT2XjQYsogbLvFSro5/nzYe5cPZ5+Wi0mzztP5TNmZhnkMhgzM9u+XXghVKoE114Ln3+uRyI3V+0ea9fW82Rl1H32URC+665w4IHa9te/wrPPpldI7d8/XUZz663w8MOarNqypTL4LVuqNWQS9JuZbQMH62Zmtv074ww45RSVq8yaBeXKKbieOBG6ddOk0i5d4JdfdPxzz2m8+mqV0SxYAPfdp8D7oIPg9ddhhx2gYUO48UZ1p7noIhg6dP33bd4c7rlHrzEz2wYO1s3MrGTIzdUE1KOP1vOuXVWDPmWKFkLKa+1a6NlTCyiBsuyrVsFhh8H//qdt++2ncepU+Mtf0q89+GCV0Tz3nPYdfjiMHavtZmZbKWM16yGE+iGEYSGEuSGEVSGEOSGEu0II1bfw9RVDCGeGEB4LIcwIISwLISwJIXwQQvhzCKFMpj6rmZkZtWppgum990KLFlCmjOrSy6T+uqlRI33sjz9q/O47WLpUiyY1baptl16qjPwee+j5H/6gDPs338D55yvIP/poqFpV5z/wQBg2TNvNzDYjI8F6CGEPYBJwHvAe0B/4AvgT8E4IoeYWnKYDMAI4EvgYuBt4DKgH3A6MDyGUy8TnNTMzAzRh9JJLlF1ftUqB+MiRKnf529+0CNK116qdI8CMGQq4BwzQ86lTFfBXqQL162tbEuSXLp2uV1++XAH98uXw3nsK4jt1gsWLC/d6zazYyVRm/V6gNnBFjPHEGOO1McZDUdDeGOi3Bef4ATgL2CnG2C11jouARsBkoB1wWYY+r5mZ2cZ166ZJp8liSf/8p2rUE0OHpktgkpKYtm3hjTdUC3/ssdp2xx06tlQpPf/LX2DhQnjoIQX277yjY//2N7j+enj0UQXzZmZ55DtYT2XVOwNzgHs22H0TsAw4O4RQ8ffOE2OcEmMcGWNcvcH2JcAdqacd8/t5zczMNqtrV5gzR7XqffpA377pWvcrr1TAvWwZrFihbePHa7zgAmXWV6+GO+/UtuOO01ipElSvDuecoyA+BLWQvOkmTXDt3l192wcPLswrNbMsl4kJpp1S49gY47q8O2KMS0IIE1Aw3wZ4dRvfY01q/HUbX29mZrZ1SpeGE0/UA5T1Pu44eO019VQ/77z0satXw5FHwu236/mbb8IPP6iM5qOPtK1VK42zZqk7TbKI0oEHwlFHwZgxytRfconO1727vgzUqqXPYmYlUibKYBqnxs82sX9WaszPusw9UuOYLTk4hDBpYw+gST4+g5mZlWQVKiigHjYMWreGnByVuFRM/cNxrVrpGvWfftK4di18+aX6tR91lLZde63KYfbaS89bt4abb1aP9yFDtO3KK5WFr1tXizJdfrkWcDKzEicTwXrV1LipWTLJ9mrbcvIQQk/gKGAKMGxbzmFmZpYRpUsro/7ee1oYac0aZdrLl9fE1AYN4Ior4IkndPxnnymoHzxYgf3336cXVmreXMfssIPGGOGDD9I/5+Zq35IlMGiQMvNJlt7MSoys7rMeQugK3IUmn54UY1yzmZcAEGNstYnzTQJaZu4TmplZiZVk0Q84AF59VfXqn34Kd9+9/nHXXZfOqn/yibLtrVsraAc49VSNQ4boUbq0vgSccoq+AEydCn/+szrSHHaY+rYvX65s/XnnaaVUM9tuZSJYTzLnVTexP9m+aGtOGkI4Efg3MA/oFGP8Yts+npmZWQFr2xY+/li16u+8A+vWaYLqAw/AbbcpAO/ePb1C6pQpCsi7doXGjZVJ799f+049FUaMSPd7b95ck1xff10rqY4enX7fQYPU1/3RR9PlOGa2XclEsD4zNW6qJn3P1LipmvbfCCGcjHqs/wAcGmOctZmXmJmZFa0Q4JBD9AAF4GXKwD33qOPLTTelj12zRmUtw4fr+cyZeuywg0aAdu00zp4NXbqo7AaUSb/hBn0xGDpUHWtOPlmtIX/5RR1lWrVKZ/7NrFjLRM16ql8VnUMI650vhFAZaA8sB97dkpOFEM4ERgFzgUMcqJuZWbEUgkpiXnlFHWVq1NDiSbVra3+MqkeH9FiqFLz/vlY7PeMMbbvlFli0CPbfX8/r1FE2vX9/ZfHLloWXXoJDD9X7tG4Ne++9fgbezIqtfAfrMcbZwFigAb9dtKgPUBF4NMa4LNkYQmgSQvhNZ5YQwjnAI8DXwMEufTEzs2ItBNWYP/20SlgWL1YN+u67w+TJsNtucPzx8K9/6fgfftBrhg5VWcvy5fDYY9qXLMSUrJS6dq0WVFq1Ss+rVtUiS3XqwPTpcNpp6dIaMyu2Qkz6vObnJFoYaSJaxfRZYDpwIOrB/hnQLsa4IM/xESDGGPJs6wSMQ18ghgHfbOStFsUY78rH55zUsmXLlpMmTdrWU5iZmeXf999Dz57wzDOqb8/rhBMU3IegEpiGDdXCcflyZdgnTlSN/EMPaYJppUqwdCm0aaNM+5o1Kr256iqdr359Ze533FHZ+osuUkBvZgWqVatWTJ48efKmGp9sqYx0g4kxzg4h7A/8DbVZPAb4HhgA9Ikx/rwFp9mVdKa/xyaO+Qp1hzEzMyu+dtoJnnpKvdPffFPZ8RUr1F/92WcVsF90kdo+goL7GLXwUps22jZokMazz4b77ktPMC1dWj3cc3NV5/7tt9q+eLH6uQ8cCC++qMWYzCzrZax1Y4zxG+C8zR7I+hn1PNseAh7K1OcxMzPLervsAmedlX5eu7a6xjz/vB6JGBWAjx6tjPvSpTBpkiawzpihY444QuOsWappTyakNmyolVE//BD69YPx4xX0X3CBsvU1a6oDzT77FM41m9lWycQEUzMzM8uEU06BL75QBrxtW2jRIl2r/t13mqy6dq1KXUBB/PjxWl31/PO1beBAZekPP1zPS5fW5NbDDoMnn1Rwvngx3HGHMvJ9+0KzZuo4s3BhoV+ymf0+B+tmZmbZpG5dtXmcOFH92D/4AE4/XW0ZTz5Z2fjOnXXsmjXqIDNyJNSqpW2jRmls3Fhj06bpY088URNdAapVU7eaiy5SCc2LL2rxpqlT9QVgypTf1tObWaFzsG5mZpbNcnK06FH//uoeM3euAvjEHnuke7uvW5cOxkeM0HjhhRpHj4a33kpPLi1TRpNcBw9W95gddlDbyBYt1AZyv/2gUSNl3zPQjMLMto2DdTMzs2xXqpQmn37+uTLf77wD06apBeRnnymL/te/asXUZOXTxYvVyjEph7n/fo2nnaaxZs30+Z97DubPT79Xhw7K8M+eDZdeCpdd5oDdrIg4WDczMysucnJUX96mjSaEjh8PBxygQPu22+Dii2H1ah3boIGy6UlHmU8+0Zi0L06C9hkz4Ior0u9RqpQ61Hz9tbLzZcsqu96gAVSvrjKcyy9PT2w1swLlYN3MzKy42mUXePddePtt6NVLk0wvuUTZ9Tlz9HzKlPTCSaBSmKpV0+Ux996r8plTT9XzJDNfqpRWQ61QQc+//lp93r/5Rm0jmzVTrbyZFaiMtW40MzOzIhACtG+vR+LIIxV8//vfeuRVpozaQia16+PGaaxeXePBB2tcuRKOPhp+zrNUyty5egwYoDr67t2V3V+zRpNUjzlGrylVqmCu1awEcmbdzMxse3PCCapt79lTK5fm5qa7xcSohZKSTi8rV2ocNkzjZZdpfPxxtZHcay+1fwSoUgVatYIHH1Rmfd06/fzIIyqVOe44aNIEPvqo8K7VbDvnYN3MzGx71KiRWjP+8IMy3/Pnw1VX6eczztD+k06CH3/U8atXq43j0Ufr+WOPaTzmGL2mbt10Scwll2iCKyizP2gQ/P3vqmv//HPo1EmTVkeP1oqsSYcaM9tqLoMxMzMrKe64Q+0f//UvdXqZPTu9r0oVuOYaBd8A8+ZpfPFFjX/8o/ZNnapserlyUKkS/PQTHH887LwzXH21Osl88IGy+4myZeHMM+H229PlNma2RZxZNzMzKylCUCeXL79Urfnjj8PYsap3/+UX9Va/6iotrLR4sV4zfTrsuqtKagCGDtV4xhmqZw9BCywBvPQSfPhh+v2OO0494FevVpnNIYdoldSff4alSwvvus2KMWfWzczMSprcXOjYMf28dWutkjpmDNx11/rHliunIDypeZ8+XeMvv8DaterlXrkyLFkC552nbTVqKCjv10+17TNnKnCfNk0dbJYt0zlattSXgO7dPSnVbBOcWTczMyvpqlVTQP7+++q5fvLJcO65CtBXrlQJzKuvqgXkmjV6zZNPKqt+9dV6PnKksvFt26bbP5Ytq7FCBVixQj8vW6bymTJlYPJk6NFDnWt+/bVQL9msuHBm3czMzGT//fVITJsGnTvDhAnplVDzuu8+lbaA+reDusW8845q2PfYQ91nTjlFHWjKlVPwP2aMjhs1Sv3hn3pK2f0QtIhT+/Za4GmvvQr+ms2ynDPrZmZmtnHNmqkNY58+mphaqpQmouamcn2zZqVrz5PM+COPaLzkEh3/7rt61KwJe++tfWvXKnA/+2w48EBtmzJF9e6TJsHAgdC0KfTtW3jXapalHKybmZnZptWuDb17q+f6r7+q1GXUKAXid9wB9erBEUdowiqolv3ww5UxB3j6aY3duikgz81VL3aAa6+Fl19Od6C5+254/XWV3eTkwI03qkzmyiv1GDky3RferIRwGYyZmZltnW7d1EWmd2+VyCSroCYuuCBdr550lZkwQRn1bt30BWD+fAXnIajOfeJEBf6HHKJHbq7KbIYPX//cV10FgwdD164Ff51mWcDBupmZmW29Qw/VY+ZMtYKsUAFeeUWlK6edpl7sRx0Fn36q4z/+WD3W+/XT89Gj1dLxmGPS7R7r1dP47LMKyBM9ekDDhnrNRx8p4B86VF1o1q2DffeFxo0L79rNCpGDdTMzM9t2jRunA+UOHaB8ea1m+soreiRCgCFDtHIqaMJpsv3771Ua07q1su9/+pMmpjZvrkWY2rdXwH7ttWr1eO+9cP7563+Ojh2hf38F7mbbEQfrZmZmlhkhwHXXqZPLY49pAmq5cmrROG6catGnT9eKpwsX6jUvvKCxd2+9fuxY+Oor2H13qFpV+6pU0fjll/Cf/6Tfr3VrqFtX5379dTjoILWYrFtXLSbr1UuX45gVUw7WzczMLLNq1EiveArqsX7aafDccwrKe/de//jevbUoE6hcBuCAA+Df/1amPmkbedll8MMPCsK/+07n7NVLdfEXXKDe7x06pHvBV62qfvHXXAM77VSgl2xWUNwNxszMzApW+fLwzDPKmp90kvqnN2+u1UxBQfarr6r0JekM8+yzGnv00KJNn3+u/uzlyikgByhdWmPZsrBggX5es0aZ+Pr1FcQPGKDAf/bswrteswxysG5mZmYFLwS1eHzySU06/egjeO89Be6ffqrsefXqatcIysZ36AC33abnEyZoPOIIePFF/XzwwRpvvFGtIytW1PMrr4RvvlH5Tdu2qo9v3Rp23FHZ9gMOUP18sqqqWRZzsG5mZmZFY8cdtdrpzTerznzxYvVRL1dO+ytWhGXL9HOy6NKkSerl3r49tGih/UOGaN/JJ2uMUeN++2niKcDPP8O8eXrt++/DRRdBu3ZqIWmWxRysm5mZWdGpWhVuukmZ8B9/hJ9+gg8+UJZ9zBiVs3TpolaQAHPnqiZ+6FA9f+stBeCtWimQB628CjBiBNxyS7q05oILdP6RIzWBdcoUaNMGjjxSWfxzzoE330wH+2ZZwMG6mZmZFb2cHC2WVLMm7L23Mu7HHKNe7C++qOeJI49Mt4BculTjihUwbZrOccIJCrhvuUX7kox76dI6/xlnqL1kCFqZdexYePtteOQRLch07LHp85oVMXeDMTMzs+zTuLHaOn75pWrPQZNHu3eHUaO07bTT0mUsyeJLd90FZcqoP/unnyp4T0podt1V46RJmriaZNA7d1YP99deg0GD9OXgyCNVJrN0qSbCnnUW7Lxz4V2/WYqDdTMzM8teu+2mR6JmTTjvPK2c2qfP+seeckq6BWQSxNerp84ypUop4AZl1VetUhb9jTdUctOpkx4dOyp4nzhRj8QNN6jOfcCAdBcas0LgYN3MzMyKjyOOULb9+edVGrN2rR4DB8Ljj+vnc85RP3aADz/U2LOnAvf58/Xa0qXVPvKNN6BWLR3z44/6IrBunZ43b66FnN5+G556Cu67T68/5hjVydetq3r6ChUK/7+DlRghlqBJFCGESS1btmw5KZmAYmZmZtuHIUO0aFJS8pJXu3YKynNzFby3bKmWkfPna8LpW29p9dM//xnuvFMlODNnKsP+8ss6xxtvwGGH6ctAXtWqwV/+ojKaHE8FtLRWrVoxefLkyTHGVvk5j/+vMjMzs+LvwguVce/dW+Ut7dppBPVz79MHvvoqXaf+2WcK1Nu1UxvI1ath+HDt69pVY6VKGlevVnvJJFCvV0+Z+tatYdEiuP56uOIKePdd1dm//346O2+WTw7WzczMbPtQv76C8tdf1yJK48fD//2fsu19+0KDBmrxCAq869dXeUsIKpv5+WeoU0ctI0FdYQAeeEDnrFkz/T53360vAUk9/D33aAGmY4/VoktNmqSDf7N8cLBuZmZm26cQ4B//UNDetat6upctq1pzUFZ87FhlzpNJowsWqFSmdm049VRtu+8+jRdcoDE5NkYYNy6dca9YEY46SuefNUsdZ3r3VrnNp5+qJt5sKzlYNzMzs+1bx47KoC9apBVSv/lGnWGWLtVk1B13VM06qD1kuXLw9NOaOLpsGXzyidpBzp6tYw4+WOPLLyvDXqaMnterBy+9pHKbIUNUw/73vyvw33tvZe07dlSpjNkWcrBuZmZmJUtODjz8MNx/v4LoRYu0OFKpUtpfseJva87XroUnn9Qk1Qsv1LZBgzQmz5OVUnNz9R7JOXJytIhT+fKaqHrssXDHHcrML1v220mrZnk4WDczM7OSJydHQfa0afD11zBjBsybp8WQFiyADh1gv/202mmpUumAeuDA9OJKr72WPhek6+E//VQ92RO1a6u7zA8/qHYe4OqroXJlTWItX1494vOu0mqW4mDdzMzMSq4QtDJp48ZQo4YmjF5zjVoyTpkCzz2XDtR32EF93hNr1mgcMkTjxRdrvOcevSapeU/aSVaponKbpOZ92TKV3KxZA088oa40gwcX7PVaseNg3czMzCxRtizceit8951q0p98Et58Ew48UBNF99oLunVTl5myZfWalSs1mTSpe//vfzXuuafGJk00zp8PJ5yQDvLLl4cVK1RD36uXymIuuQQaNtSXhfr14dJLlam3EsvBupmZmdmGKlTQokgnnaSSmLFj4fTTVYf+1FMK6Jct07HVq2siaVKznmx/8EGNSUnMgw/C4sWaZAoK8mNUUH7xxcq8gyayLl6sLwz33aeVVB96qDCu2rKQg3UzMzOzzalSBR57DObM0cTSvn0VSDdtqv7s++yjFVCHDUvXsH//PbRpo3p0UJAP0KmTxgYNFOCvWgXHHAO//KLtOTl67eTJcN55Kqnp0UN93Js00Qqs11+vWnvb7oWYrORVAoQQJrVs2bLlpEmTivqjmJmZ2fZg3jwF42+88dt9lSppAmuDBnresKGy5s2aafvf/w433AAjR6qVZKNGyqYvW6YvANWqabJrs2YK3jdUpowWXjrjjAK9RNs2rVq1YvLkyZNjjK3yc57cTH0gMzMzsxKndm0tuvT++zB6tILratXgmWfUb71jR7jiCnWWSUybli59ARg1SuNpp8Hf/qbWkZUrq0TmpJPWD9QnTlQwP3iwMvVnn62M/y+/qIb+sMPg/PM1Gda2Cw7WzczMzPIjBDjgAD0SV12lfuoff6zymLxKl1aXmVq19Hz+fI0TJmhM2kW+/roy9rVqKYs+d64WVtptN9XRf/yxWkLmXWRp3DgF/A89lC6/sWLNwbqZmZlZpu26K3z4oTrDjBypcpmqVeF//9PP55wD116rmvakJPnVVzWxtVcvPX/kEY3nnKP+7iFoMiuoR/zMmen3e/xx7R86VF1sTj9dXwiWLtUiTYccAt276zNYseJg3czMzKwg5ObCiSfqkZg1SwsvTZsGZ565/vE5OSqlSVo9zp2r8Ztv1O7x6KNVYjNjhgL5cuXUI37WLNh9dy3K9Ic/aCLq++/rS0LiqafguutU496tW8Fet2WUg3UzMzOzwrLnnjB1KowYoYB77lzVp3/7LSxaBP36qfa8Q4d0V5kka3711Xr+8MMaTz9diziBgniAm29WoJ4YOFATXR9+WCU1p5yirPzKlTp/27Yqu6lYsVAu37aeWzeamZmZFaZKlTS5dOJEtYKcNk316nXrwrvvqr97+fLw0kvp1wwYAIceqp/nzNEYAixcqG4xu++u2vd//Uv7mjXT2LSp2j+OHw+HH66Sm/vvV/A+fLgC93r1tIKqZSVn1s3MzMyKWtOm8NFHCqSHD1cnmUqVVP6ybBn85z+qb2/dWpNNIZ1h79VLgfuIEbB6NXTpkq5nTzLmDzygyaeJ66/XZNWRI/UF4dRT4Z130qur7r+/svDlyxfO9dsmObNuZmZmlg1q1VIQ/fnnCpp//lkBdO3a6gxzwAFanGnECB2/di307KkJqKAe7qC2kJ9/rmC8VStYsUKTWQFatNC477567cSJ0LWrMu79+2vBp0GD4NxzlXEfPbow/wvYRjizbmZmZpatmjXTSqZ33aXVURcu1PZy5VR3/tlnyqI3afLbjPtll6lN5OOPK/Bv3VqTXiGdMX/+eXj66fT7XXyxSmqeeEK176edBlOmwLp1+nKw777q/e6Me6FxZt3MzMwsm9WrB7fdppr0hQth+XK1gKxZE8aOhb32Uu/1oUN1/MqVcMwxcM01ej5jhsaWLZWpr1AB2rdX8H3llcqqN2+ePuYvf9H5zMssgwAAEyxJREFUzz1X2269VbXwd9yhRZjq109n963AObNuZmZmVhzk5KT7rDdvDh98ALfcosA5mXRapozq1teuVaeZXXdNZ9yTlVK7d1f3mLFj4csvFeg3aKAuNWXL6piJE9PHgzLs++yjLPykSQrap09Xpn7NGtXcO+NeIJxZNzMzMyuOGjTQhNT581UO89VX8N57UKOGFkbabTfYbz8dA/DLL3qedIz55BONhxyizjMh6GfQCqyrVilAB73u+uv1BeGKK7TtH//Qaqm33KLgvV49ePDBQrv8ksKZdTMzM7PirEIF9W8H2GUXlbDcfLPqzqdM0fZSpZRtr1kTlixRb/fSpbXv+eeVHT/hhPTKq++/ryx+q1bw8cfpYz/5BB56KP3eXbqoFv6//1Ugf8EFWqSpUiWV4+y5pxZhch/3bebMupmZmdn2pGFDlcZ8/73aMk6apOC7Zk21b9x1Vzj4YBgyRMcvWKAg/9579XzqVI2HHppedCnJuF99tTL0ySqrzZvDTTfp/DfeqG3//Kd+7tcv3VXm7rtVG29bzZl1MzMzs+1RjRpw4IHp5+++q0mnzz4Lb72lbSEoiG7QIL1iatIx5q23tKpqmzaaeDpnDowZo7r2I47QxNVSpXTsnDnpchtQcN+xo8px3n1XpTNffKE2lMuWqeNMt25qRWm/y8G6mZmZWUnQsCE89ZQy7h9/rOC8cmU49lh4801l1zt2VF92gHnzVAozbJieT5um8eCD4Zln9HOHDhpvuEHH77mnymCaNFEpzs03q397r15qP5nXn/4E112nHvAhFPDFF18O1s3MzMxKkp120iMxcaLKW55/Hl55Zf1jGzZMd6BJMu8ffZQOzA8/XGU0TzyhgLtrV5XBJBn3H3+EAQPS5zvgALWVfO01fUG47rp0R5olS2DnnbVyas2aBXf9xYyDdTMzM7OSrGFDZcq/+UYLMIGC5ZNPVi36Lruo7CUxb54WZXr4YQXw06erXeT++6urDEC7dhr79VOXmt12U1DeoIFq3G+6CYYPhx494IEH1v88vXop696vXzroL8EcrJuZmZmZsto775x+PnGiFk16/nl48cX1j23YUIE3pDPuc+bATz/BDjuoHn3FivRqqmefrTaPybGLFqVbSIJWaj3lFHj7bdW5//OfqnFv0UKrr+60k3q916tXEFee1Rysm5mZmdlv7babJqN+9ZXaQa5dC3XqqMPLxx+rq8xRR6UXQvrpJ2XChw/XJNRPP1XnmN13V8kLpDPud96pCaq77AJff63z3nCD9j39tIL9J57QI3HNNXD++TBwYHrxphLAwbqZmZmZbdquu+qRmDABevaE555T1j2vBg3UzhHSWfQFC5Qlr1hRq6euXZsufTn/fJXEJMcuW6YM/Lp1et6okUpl3n9fpTpDhqicpl07WLhQWfxTT9Vx2ykH62ZmZma25erXV+D81Vdq77hmDdStC5dfrk4wu++ujHv16grCFy/W6wYPhqpV1Y3mhx/UWvLDD7UvybgPHqyFnOrXh2+/Vbeaa67Rvjfe0ITWV15ZfyJs797KxA8bpuO3MxkL1kMI9YG/AUcBNYHvgWeAPjHGn7fiPDWA3sCJwE7AAmAM0DvG+G2mPq+ZmZmZ5cOGGfe334bLLlMZy3//u/6xO+2U7vmeZNGXL1fQn5urlU8h3av9oou0sFIywXTVKrV4/PXX9HtfeaUWcBo1Cp58Uhn3ww9XOU716qqBb926YK69EGUkWA8h7AFMBGoDzwIzgAOAPwFHhRDaxxgXbMF5aqbO0wh4Dfg30AQ4D+gSQmgbY/wiE5/ZzMzMzDKodm3VmH/7LYwfDytXakLo9dcrW96kCXTurMA9N1f7QX3Y69bVhNRZs7Rv9mzta9tW46OPanGlOnWUlS9VSsE6KKPftq1Wap00Kf15br9dizONHg077lh4/x0yLCdD57kXBepXxBhPjDFeG2M8FOgPNAb6beF5/oEC9TtjjIelznMiCvprp97HzMzMzLJV/frq/vLHP6qn+vjxcNZZCrDHjNEE1CRDXr26FlmCdBZ97Vp46CH9fPHFGpOM+6WXrn/sr7/CVVcp8w4K5u+/X4F8tWrp0pmlSwv0kgtSvoP1VFa9MzAHuGeD3TcBy4CzQwgVN3OeSsDZqeNv3mD3IOAr4MgQwu75/cxmZmZmVkiqVVNm/OuvNd5/v8pkDjpIbRlbtIBDD1VgXrYsxKjX9e2rbDyo+wxokSWA9u01PvWUAvLatfV85Uq48EJl62fM0MTTjz/+bS/3YiQTmfVOqXFsjHFd3h0xxiXABKAC0GYz52kDlAcmpF6X9zzrgJc3eD8zMzMzKy7q1FGG/cILoUsXZdkvvlgLLI0fr4x7kiGvWFElLIncVOX24MEakwz7kCEaL7ts/eNApS+33rr+ccVQJmrWG6fGzzaxfxbKvDcCXs3neUid53eFECZtYleTzb3WzMzMzApBxYpw331aqfSVV2DJEtWuDx6slpAdOmhSaqNG6Wz72rXw17+mJ45On67x51Qvk6SkJnHssRpnztRri+GKqJkI1qumxsWb2J9sr1ZI5zEzMzOz4qJGDfVKTxx+uNox3nefFmP63//S+0qX1mTSGCEEPQcYNEhjkmFPLEkVa+TmprvQFDPbZZ/1GGOrjW1PZdxbFvLHMTMzM7MtVaaMylduuAHGjYNFi1RC88QT6qX+hz9A06awzz7aB5po2rMndNqgWnrYMI2HHKLgvhjKRLCeZLyrbmJ/sn1RIZ3HzMzMzIq7SpXgxBPTzzt3VklM//7w6ad6JHJytHLqunUqdYkR/vMfZehBgXwxlYl/D5iZGjdVS75natxULXqmz2NmZmZm25ucHK1m+vXXMHYsPPaYMu/XX68g/cILoUEDOO44BfXduql3+x//CMcfX9SffptlIrM+PjV2DiHk5O0IE0KoDLQHlgPvbuY87wIrgPYhhMp5O8KEEHLQJNW872dmZmZmJU2ZMnDEEennhx0Gu+8Ot9wCn3+uRZlACzL16qWe68W0BAYykFmPMc4GxgINgA2q+ukDVAQejTEuSzaGEJqEENbrzBJjXAo8mjr+5g3O0zN1/pe9gqmZmZmZradHD3V8eecdeOYZePNNmDNHwXoxnViayNQE00uBicDAEMJhwHTgQNQT/TPg+g2OT/XZYcOvOdcBHYFeIYR9gfeAvYATgHn89suAmZmZmZmC8jabW9an+MnIV41Udn1/4CEUpP8Z2AMYALSJMS7YwvMsANoCA4GGqfMcCAwHWqXex8zMzMysRMhY68YY4zfAeVt47CYLh2KMC4E/pR5mZmZmZiVW8S7iMTMzMzPbjjlYNzMzMzPLUg7WzczMzMyylIN1MzMzM7Ms5WDdzMzMzCxLOVg3MzMzM8tSDtbNzMzMzLKUg3UzMzMzsyzlYN3MzMzMLEs5WDczMzMzy1IO1s3MzMzMspSDdTMzMzOzLOVg3czMzMwsSzlYNzMzMzPLUiHGWNSfodCEEBaUL1++xl577VXUH8XMzMzMtmPTp09nxYoVC2OMNfNznpIWrH8JVAHmFPFHAWiSGmcU6aewguL7u33z/d2++f5u33x/t3/Zco8bAL/EGHfLz0lKVLCeTUIIkwBijK2K+rNY5vn+bt98f7dvvr/bN9/f7d/2do9ds25mZmZmlqUcrJuZmZmZZSkH62ZmZmZmWcrBupmZmZlZlnKwbmZmZmaWpdwNxszMzMwsSzmzbmZmZmaWpRysm5mZmZllKQfrZmZmZmZZysG6mZmZmVmWcrBuZmZmZpalHKybmZmZmWUpB+tmZmZmZlnKwXqGhBDqhxCGhRDmhhBWhRDmhBDuCiFU38rz1Ei9bk7qPHNT561fUJ/dNi+/9zeEUDGEcGYI4bEQwowQwrIQwpIQwgchhD+HEMoU9DXY78vUn+ENznlwCGFtCCGGEPpm8vPa1snk/Q0htEz9Wf42da4fQwhvhBC6F8Rnt83L4N/BB4UQnk29fmUI4esQwoshhKMK6rPb7wshdAsh3B1CeCuE8Evq9+mIbTxXxn/PFwYvipQBIYQ9gIlAbeBZYAZwANAJmAm0jzEu2ILz1EydpxHwGvA+0AQ4AZgHtI0xflEQ12Cblon7m/pF/xKwEBgPfA5UB44H6qTOf1iMcWUBXYb9jkz9Gd7gnJWBqUAtoBLQL8Z4QyY/t22ZTN7fEEJPYADwM/AC8B1QA9gH+DbGeFrGL8B+Vwb/Dr4EuBdYBjwNfAvUB7oCFYAbYoz9CuIabNNCCFOAFsBSdE+aACNjjGdt5Xky/nu+0MQY/cjnA3gZiMDlG2y/M7V98Bae5/7U8XdssP2K1PYxRX2tJfGRifsL7AucCZTZYHtlYFLqPH8u6mstqY9M/Rne4LXD0Jez61Ln6FvU11lSHxn8Hd0ZWJc6X+WN7C9d1NdaEh8Z+h1dGlgErAAab7BvL2AlsBwoW9TXW9IeKJjeEwhAx9Q9HVEU/58U1cOZ9XxKfVP7HJgD7BFjXJdnX2Xge/Q/WO0Y47LfOU8llD1fB+wUY1ySZ18O8AWwa+o9nF0vJJm6v5t5jzOAkcB/Y4zH5ftD21YpiHscQjgBeAY4G8gFhuPMepHI5P0NIXwENAR2idmagSthMvh38I7AD8DUGGOLjeyfCjQDavneF50QQkf0r9NblVkvjL/LC5Jr1vOvU2ocm/fmA6QC7gnon8/abOY8bYDywIS8gXrqPEkmJ+/7WeHI1P39PWtS46/5OIdtu4ze4xBCbeAB4JkY4zbVVVpGZeT+hhD2AZoDY4GFIYROIYSrU3NODkslVazwZerP7zxgPtAohLBn3h0hhEYoszvFgXqxVRh/lxcY/3LJv8ap8bNN7J+VGhsV0nksswrjvvRIjWPycQ7bdpm+xw+g360X5+dDWcZk6v62To3zgNfRvKLbgNuBccCUEELDbf+Yto0ycn+jygwuQ392J4UQHg4h3BJCeASVKn4CnJyBz2tFo1jHWLlF/QG2A1VT4+JN7E+2Vyuk81hmFeh9SU1WOwqYgmqcrfBl7B6HEHqgScOnxhh/zMBns/zL1P2tnRrPR5NKuwBvAzsCvYGzgBdCCM1ijKu3/ePaVsrYn98Y4xMhhLnAKCBvZ58fUSmbS1CLr2IdYzmzblZEQghdgbtQneRJMcY1m3mJZbEQQgN0P5+IMT5etJ/GCkDy92Up4LQY44sxxl9ijLNQYPcBysqdVFQf0PInhHAW+leSt9Ck0gqp8VVgEPDvovt0VpI5WM+/5NtY1U3sT7YvKqTzWGYVyH0JIZyIfvHPAzp60nCRytQ9HoY6SVyaiQ9lGZOp+5vs/yHG+E7eHakSimdTTw/Y6k9o+ZGR+5uqSx+Gyl3OjjHOiDGuiDHOQBPFJwEnpyY4WvFTrGMsB+v5NzM1bqrOKZmosqk6qUyfxzIr4/clhHAy8AT6p9VDYowzN/MSK1iZusctUanE/NSiHTGEENE/nwNcn9r2TP4+rm2lTP+O3tRf5j+nxvJb+LksMzJ1fzuj9o1vbGQC4jrgzdTTVtvyIa3IFesYyzXr+Tc+NXYOIeRspB1Qe9Sb9d3NnOddlJVrH0KovJHWjZ03eD8rHJm6v8lrzgQeRjWvnZxRzwqZusePoH8239CewMFoXsIk4MN8f2LbGpn8Hb0MaBBCqLiR9m77pMYvM/CZbctl6v6WTY07bGJ/st3zEYqnjP5dXticWc+nGONs1MqrAZpJnlcfoCLwaN5f7CGEJiGEJhucZynwaOr4mzc4T8/U+V92cFe4MnV/U9vPQQHd18DBvpfZIYN/hq+IMV6w4YN0Zv2F1LZ7Cuxi7DcyeH+XAw8C5YC+IYSQ5/hmwLmo/eqTmb8K25QM/o5+KzV2CyE0z7sjhLAv0A0tnPNa5j69ZVoIoXTq/u6Rd/u2/H+STbwoUgZsZAnb6cCBqK/nZ0C7vL1ZU/80TowxbHCemqnzNEK/EN5Dk1tOQLXN7VL/w1khysT9DSF0QhOXclBd5DcbeatFMca7Cugy7Hdk6s/wJs59Ll4UqUhl8Hd0FeANtCLx/1Bv5h3RcvTlgStjjAMK+npsfRm8v8OA81D2/GngKxTcnQiUAe6KMV5VwJdjG0jN8Tox9bQOcCTqzJN8wfopxnh16tgG6F+3vooxNtjgPFv1/0lWydRSqCX9AeyM/kL+Hv1B/wp1hqi+kWMjqTlJG9lXAxiQev3q1PmGAfWL+hpL8iO/9xdl3eJmHnOK+jpL8iNTf4Y3cmxy7/sW9TWW5EcGf0dXAvqhv9xXoRr2sUDnor7GkvzIxP1FK1iei/ro/4z+pWQh6gZzWlFfY0l9oGqDLfq7E3252uTfp1vz/0k2PZxZNzMzMzPLUq5ZNzMzMzPLUg7WzczMzMyylIN1MzMzM7Ms5WDdzMzMzCxLOVg3MzMzM8tSDtbNzMzMzLKUg3UzMzMzsyzlYN3MzMzMLEs5WDczMzMzy1IO1s3MzMzMspSDdTMzMzOzLOVg3czMzMwsSzlYNzMzMzPLUg7WzczMzMyylIN1MzMzM7Ms5WDdzMzMzCxLOVg3MzMzM8tS/w/Lpg1B+Z6sSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt1\")\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt2:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ZDT2\n",
    "\n",
    "This is also a 30-variable problem ($n=30$) with a non-convex Pareto-optimal set:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\begin{split}\n",
    "f_1(x) &= \\, & x_1 \\\\\n",
    "g(x) &=& 1 + \\frac{9}{n-1} \\; \\sum_{i=2}^{n} x_i \\\\\n",
    "h(f_1,g) &=& 1 - (f_1/g)^2 \\\\\n",
    "\\end{split}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "$$0 \\leq x_i \\leq 1 \\quad i=1,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optimum**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$0 \\leq x_1^* \\leq 1  \\quad \\text{and} \\quad x_i^*=0 \\; \\text{for} \\; i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt2\")\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt3:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ZDT3\n",
    "\n",
    "This is also a 30-variable problem ($n=30$) with a number of disconnected Pareto-optimal fronts:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\begin{split}\n",
    "f_1(x) &= \\, & x_1 \\\\\n",
    "g(x) &=& 1 + \\frac{9}{n-1} \\; \\sum_{i=2}^{n} x_i \\\\\n",
    "h(f_1,g) &=& 1 - \\sqrt{f_1/g} - (f_1/g) \\; \\sin(10\\pi f_1)\\\\\n",
    "\\end{split}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "$$0 \\leq x_i \\leq 1 \\quad i=1,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optimum**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$0 \\leq x_1^* \\leq 0.0830 \\\\\n",
    "0.1822 \\leq x_1^* \\leq 0.2577\\\\\n",
    "0.4093 \\leq x_1^* \\leq 0.4538 \\\\\n",
    "0.6183 \\leq x_1^* \\leq 0.6525 \\\\\n",
    "0.8233 \\leq x_1^* \\leq 0.8518 \\\\\n",
    "x_i^*=0 \\; \\text{for} \\; i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 388
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt3\")\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt4:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ZDT4\n",
    "\n",
    "This is a 10-variable ($n=10$) problem having a convex Pareto-optimal set. There exist many local Pareto-optimal solutions in this problem. Therefore, algorithms can easily get stuck in a local optimum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\begin{split}\n",
    "f_1(x) &= \\, & x_1 \\\\\n",
    "g(x) &=& 1 + 10(n-1) + \\sum_{i=2}^{n} (x_i^2 - 10 \\cos(4\\pi x_i))\\\\\n",
    "h(f_1,g) &=& 1 - \\sqrt{f_1/g}\\\\\n",
    "\\end{split}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "$$0 \\leq x_1 \\leq 1 \\\\\n",
    "-10 \\leq x_i \\leq 10 \\quad i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optimum**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$0 \\leq x_1^* \\leq 1  \\quad \\text{and} \\quad x_i^*=0 \\; \\text{for} \\; i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt4\")\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt5:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ZDT5\n",
    "\n",
    "In ZDT5 in variables are decodec by bitsrings. At all 11 discrete variables are used, where $x_1$ is represented by 30 bits and the rest $x_2$ to $x_{11}$ by 5 bits each. The function $u(x)$ does nothing else than count the number of $1$ of the corresponding variable. Also, note that the objective function is deceptive, because the values of $v(u(x_i))$ are decreasing with the number of 1's, but has its minimum when all variables are indeed 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\begin{split}\n",
    "f_1(x) &= \\, & 1+u(x_1)\\\\\n",
    "g(x) &=& \\sum_{i=2}^{n} v(u(x_i))\\\\[2mm]\n",
    "v(u(x_i)) &=&\n",
    "\\begin{cases}\n",
    "2 + u(x_i) \\quad \\text{if} \\; u(x_i) < 5\\\\\n",
    "1 \\quad \\quad \\quad \\; \\; \\; \\text{if} \\; u(x_i) = 5\n",
    "\\end{cases}\\\\[4mm]\n",
    "h(f_1,g) &=& 1 /f_1(x)\\\\[2mm]\n",
    "\\end{split}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optimum**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$0 \\leq u(x_1^*) \\leq 30  \\quad \\text{and} \\quad u(x_i^*)=5 \\; \\text{for} \\; i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt5_no_norm"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt5\", normalize=False)\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please note that by default here the Pareto-front is not normalized. However, this can be easily achived normalizing $f_1$ in the range of $(1,31)$ and $f_2$ in $(10/31, 10)$ which are the known bounds of the Pareto-set. By default the normalized problem is used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt5\", normalize=False)\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_zdt6:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ZDT6\n",
    "\n",
    "This is a 10-variable ($n=10$) problem having a nonconvex Pareto-optimal set. The density of solutions across the Pareto-optimal region is non-uniform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\begin{split}\n",
    "f_1(x) &= \\, & 1 - \\exp(-4 x_1) \\sin^6 (6 \\pi x_1) \\\\[2mm]\n",
    "g(x) &=& 1 + 9 \\bigg[\\bigg( \\sum_{i=2}^{n} x_i \\bigg) / 9\\bigg]^{0.25}\\\\[2mm]\n",
    "h(f_1,g) &=& 1 - (f_1/g)^2\\\\\n",
    "\\end{split}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "$$0 \\leq x_i \\leq 1 \\quad i=1,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Optimum**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$0 \\leq x_1^* \\leq 1  \\quad \\text{and} \\quad x_i^*=0 \\; \\text{for} \\; i=2,\\ldots,n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "code": "usage_problem.py",
    "section": "zdt6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymoo.factory import get_problem\n",
    "from pymoo.util.plotting import plot\n",
    "\n",
    "problem = get_problem(\"zdt6\")\n",
    "plot(problem.pareto_front(), no_fill=True)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
